1. Field of the Invention
The present invention relates to a stage driving and controlling apparatus. In particular, the present invention relates to a stage driving and controlling apparatus preferably used for driving and controlling a stage on which a substrate such as a wafer or a mask (or reticle) is placed in a measuring apparatus or an exposure apparatus used in a production step for producing semiconductors. The present invention also relates to an exposure apparatus provided with the stage driving and controlling apparatus.
2. Description of the Related Art
The position or the velocity of a stage in X and Y two-dimensional directions and a rotational direction about the Z axis (hereinafter referred to as ".theta. direction") has been hitherto controlled in an exposure apparatus or the like in order to position the stage at a predetermined position. FIG. 4 shows an example of a driving system for such a stage. In FIG. 4, a stage 80 is driven in the Y and .theta. directions by first and second motors 82, 84 and ball screw mechanisms 86, 88 driven by the motors 82, 84 respectively, and the stage 80 is driven in the X direction by a third motor 90 and a ball screw mechanism 92 driven by the motor 90. In this arrangement, positions of the stage 80 in the Y and .theta. directions are detected by a Yl laser interferometer (Yl INTERFERO.) 94 and a Yr laser interferometer(Yr INTERFERO.) 96, and a position of the stage 80 in the X direction is detected by an X laser interferometer (X INTERFERO.) 98.
FIG. 5 shows an arrangement of a stage driving and controlling apparatus for driving and controlling the stage 80. In FIG. 5, a .theta. position of center of gravity-calculating block (.theta. calculation) 100 is provided for converting positional information from the Yl laser interferometer 94 and the Yr laser interferometer 96 into an amount of rotation about the Z axis at a position of the center of gravity (positional information in the .theta. direction) and outputting the obtained result. Similarly, a Y position of center of gravity-calculating block (Y calculation) 102 is provided for converting positional information from the Yl laser interferometer 94 and the Yr laser interferometer 96 into positional information on the center of gravity in the Y direction and outputting the obtained result. An X position of center of gravity-calculating block (X calculation) 104 is provided for inputting positional information from the X laser interferometer 98 and the positional information on the center of gravity in the .theta. direction fed from the .theta. position of center of gravity-calculating block 100, converting the input into positional information on the center of gravity in the X direction, and outputting the obtained result. It is noted that so-called non-interfering calculation is performed in the three position of center of gravity-calculating blocks 100, 102, 104.
The pieces of positional information on the center of gravity outputted from the three position of center of gravity-calculating blocks 100, 102, 104 are used as primary feedback signals respectively, and they are compared with positional command values in the .theta., Y, X directions (reference input signals for indicating target values) respectively. Positional deviations of the center of gravity in the .theta., Y, X directions are inputted into three motor position-calculating conversion blocks (FIRST, SECOND and THIRD P-C BLOCKS) 106, 108, 110. The pieces of positional information on the center of gravity in the respective directions outputted from the three position of center of gravity-calculating blocks 100, 102, 104 are converted by differentiating circuits (DIF.) 112, 114, 116 into pieces of velocity information on the center of gravity in the .theta., Y, X directions respectively, and they are fed to three motor velocity-calculating conversion blocks (FIRST, SECOND and THIRD V-C BLOCKS) 118, 120, 122.
The positional deviations of the center of gravity in the .theta., Y, X directions are inputted into the first motor position-calculating conversion block 106, and they are converted into positional information at a position of the first motor 82. The positional information at the position of the first motor 82 is converted by a position gain 124 into a target value of velocity at the position of the first motor 82. The positional deviations of the center of gravity in the .theta., Y, X directions are inputted into the second motor position-calculating conversion block 108, and they are converted into positional information at a position of the second motor 84. The positional information at the position of the second motor 84 is converted by a position gain 126 into a target value of velocity at the position of the second motor 84. The positional deviations of the center of gravity in the .theta., Y, X directions are inputted into the third motor position-calculating conversion block 110, and they are converted into positional information at a position of the third motor 90. The positional information at the position of the third motor 90 is converted by a position gain 128 into a target value of velocity at the position of the third motor 90.
The pieces of velocity information on the center of gravity in the .theta., Y, X directions are converted into velocity information at the position of the first motor 82 by the first motor velocity-calculating conversion block 118. The velocity information at the position of the first motor 82, which is used as an internal feedback signal, is compared with the target value of velocity at the position of the first motor 82. A difference between the both is used as an operation signal for a first controller 130. The pieces of velocity information on the center of gravity in the .theta., Y, X directions are converted into velocity information at the position of the second motor 84 by the second motor velocity-calculating conversion block 120. The velocity information at the position of the second motor 84, which is used as an internal feedback signal, is compared with the target value of velocity at the position of the second motor 84. A difference between the both is used as an operation signal for a second controller 132. The pieces of velocity information on the center of gravity in the .theta., Y, X directions are converted into velocity information at the position of the third motor 90 by the third motor velocity-calculating conversion block 122. The velocity information at the position of the third motor 90, which is used as an internal feedback signal, is compared with the target value of velocity at the position of the third motor 90. A difference between the both is used as an operation signal for a third controller 134.
The first, second, and third controllers 130, 132, 134 determine control amounts for the first, second, and third motors 82, 84, 90 respectively by means of proportional operation (P operation) or (proportional+integral) operation (PI operation). The determined control amounts are given as command values to the first, second, and third motors 82, 84, 90.
The P operation referred to herein is included in so-called basic control operations for controllers, which is specified in that an output signal is proportional to an operation signal (deviation), i.e., a control objective is operated in proportion to a deviation. The P operation is a basic control operation in feedback control. A transfer function G(s) of a controller which performs this control operation is represented by G(s)=K.sub.p provided that K.sub.p represents a proportional gain. The PI operation referred to herein is included in so-called basic control operations for controllers, which is specified as a control operation in which an output signal is a synthetic value of a control output proportional to a deviation as described above and a control output proportional to a time-integrated value of the deviation. A transfer function of a controller which performs this control operation is represented by G(s)=K.sub.P (1+1/T.sub.I /s) provided that T.sub.I represents an integral time. The PI operation has been adopted in order to solve a problem that a steady-state deviation remains in the case of the use of only the P operation. Namely, in the case of control by using a control output obtained by adding an integrated value of the deviation (PI operation), even a slight deviation produces a large feedback output with the passage of time. Accordingly, the problem of the steady-state deviation is solved. The controller which performs the P operation is herein referred to as "P controller", and the controller which performs the PI operation is herein referred to as "PI controller".
The conventional apparatus for driving and controlling the stage having three degrees of freedom has controlled the system having three degrees of freedom without interference by converting the information incorporated from the laser interferometers as described above into the position and velocity of the center of gravity, followed by further conversion into the position and velocity at the positions of the motors to perform positional control and velocity control by using the P controllers or the PI controllers provided for each of the motors.
As for an exposure apparatus, especially an exposure apparatus of the full-area exposure system such as a so-called steppers, it is an extremely important task to improve the throughput. For this purpose, it is indispensable to increase the positioning velocity including the movement velocity of the stage. However, when the stage is driven by using a ball screw as described above, the rigidity of the ball screw sometimes becomes a factor to restrict positioning for the stage. Accordingly, a stage having higher rigidity is required. In order to respond to this request, for example, it is conceived that a stage (10) is driven in directions of three degrees of freedom by using four motors (12, 14, 16, 18) as shown in FIG. 2.
However, in the arrangement of the apparatus shown in FIG. 2, the number of the motors is larger than the degrees of freedom of the stage. Accordingly, if the conventional control system including the controllers arranged for each of the motors is used, it is feared that the following inconvenience arises. Namely, interference between the controllers takes place if any error occurs, such as conversion (non-interfering calculation) errors in the position of center of gravity-calculating blocks, the motor position-calculating conversion blocks, and the motor velocity-calculating conversion blocks resulting from mechanical attachment errors in respective components such as the interferometers, ball screws, and motors, control errors in the controllers, thrust errors in the motors, and uneven movement of the respective driving units. In such a situation, it is difficult to adjust the system, the control response is lowered, and a problem such as deterioration in robust characteristics arises. On the other hand, it is almost impossible to completely avoid the various types of errors as described above.